| Résume | Horospherical products of two Gromov hyperbolic spaces where introduced to unify the construction of metric spaces such as Diestel-Leader graphs, the Sol geometry or treebolic spaces. In this talk we will first recall all the bases required to construct these horospherical products, then we will study their large scale geometry through a description of their geodesics and visual boundary. Afterwards we will get interested in a geometric rigidity property of their quasi-isometries. This result will lead to a new quasi-isometry classification for a family of non-hyperbolic solvable Lie groups. |
